On of the reddit users named slightlyKiwi gave a very interesting answer:

You really don't need to read the Keats. Or indeed know anything about sci-fi in general.However, for maximum enjoyment it can help to know one or two things:

In the first book, each of the Pilgrim's tells their own Tale. This is modelled, loosely, on Chaucer's Canterbury Tales. You don't need to know this.

Each of the Pilgrims is from a different era of the Hegemony's history(ish), and, to mirror this each of their tales is told in a different style from the history of science fiction. Brawne Lamia's, for instance, in very Gibson cyberpunk, while Colonel Kassad's owes much to classic space opera. Again, you don't need to know this.

Judaism, Islam, and Christianity have a common story in their holy books wherein Abraham is asked by God to sacrifice his only son. Abraham accepts, and God spares this life of the child at the last moment. This concept is found throughout the books. You don't need to know this.

There are lots of references to the Wizard of Oz. You don't need to know this.

In real life, a 'shrike' is a type of bird that kills more than it eats, and hangs the spare corpses on the thorns of a tree. You don't need to know this.

TLDR: There's lots to know, but you don't need to know any of it. The book fills in most of the blanks admirably.